Asymptotic Expansions for the Joint and Marginal Distributions of the Latent Roots of the Covariance Matrix

R. J. Muirhead; Y. Chikuse

doi:10.1214/aos/1176343205

Asymptotic Expansions for the Joint and Marginal Distributions of the Latent Roots of the Covariance Matrix

The Annals of Statistics ◽

10.1214/aos/1176343205 ◽

1975 ◽

Vol 3 (4) ◽

pp. 1011-1017 ◽

Cited By ~ 13

Author(s):

R. J. Muirhead ◽

Y. Chikuse

Keyword(s):

Covariance Matrix ◽

Asymptotic Expansions ◽

Marginal Distributions ◽

Latent Roots

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Asymptotic expansions for the joint and marginal distributions of the latent roots ofS 1 S 2 −1

Annals of the Institute of Statistical Mathematics ◽

10.1007/bf02532785 ◽

1977 ◽

Vol 29 (1) ◽

pp. 221-233 ◽

Cited By ~ 4

Author(s):

Yasuko Chikuse

Keyword(s):

Asymptotic Expansions ◽

Marginal Distributions ◽

Latent Roots

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On the asymptotic expansions for the bias and covariance matrix of autoregressive estimators

Developments in Time Series Analysis ◽

10.1007/978-1-4899-4515-0_7 ◽

1993 ◽

pp. 80-100

Author(s):

T. D. Pham

Keyword(s):

Covariance Matrix ◽

Asymptotic Expansions

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Asymptotic expansions of the distributions of the latent roots and the latent vector of the Wishart and multivariate F matrices

Journal of Multivariate Analysis ◽

10.1016/0047-259x(76)90002-6 ◽

1976 ◽

Vol 6 (4) ◽

pp. 500-525 ◽

Cited By ~ 33

Author(s):

Nariaki Sugiura

Keyword(s):

Asymptotic Expansions ◽

Latent Vector ◽

Latent Roots

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Asymptotic distributions of likelihood ratio criteria for testing latent roots and latent vectors of a covariance matrix under an elliptical population

Biometrika ◽

10.1093/biomet/72.2.331 ◽

1985 ◽

Vol 72 (2) ◽

pp. 331-338 ◽

Cited By ~ 23

Author(s):

TAKESI HAYAKAWA ◽

MADAN L. PURI

Keyword(s):

Covariance Matrix ◽

Likelihood Ratio ◽

Asymptotic Distributions ◽

Latent Roots

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Matrix-variate distribution theory under elliptical models-4: Joint distribution of latent roots of covariance matrix and the largest and smallest latent roots

Journal of Multivariate Analysis ◽

10.1016/j.jmva.2015.12.012 ◽

2016 ◽

Vol 145 ◽

pp. 224-235 ◽

Cited By ~ 1

Author(s):

Francisco J. Caro-Lopera ◽

Graciela González Farías ◽

Narayanaswamy Balakrishnan

Keyword(s):

Covariance Matrix ◽

Joint Distribution ◽

Distribution Theory ◽

Elliptical Models ◽

Latent Roots

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Asymptotic expansion for the distribution of a function of latent roots of the covariance matrix

Annals of the Institute of Statistical Mathematics ◽

10.1007/bf02532799 ◽

1977 ◽

Vol 29 (1) ◽

pp. 389-396 ◽

Cited By ~ 12

Author(s):

Sadanori Konishi

Keyword(s):

Asymptotic Expansion ◽

Covariance Matrix ◽

Latent Roots

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Bounds for the distribution functions of the extreme latent roots of a sample covariance matrix

Biometrika ◽

10.1093/biomet/61.3.641 ◽

1974 ◽

Vol 61 (3) ◽

pp. 641-644 ◽

Cited By ~ 2

Author(s):

R. J. MUIRHEAD

Keyword(s):

Covariance Matrix ◽

Distribution Functions ◽

Sample Covariance Matrix ◽

Sample Covariance ◽

Latent Roots

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Asymptotic expansions of the distributions of the latent roots in MANOVA and the canonical correlations

Journal of Multivariate Analysis ◽

10.1016/0047-259x(77)90080-x ◽

1977 ◽

Vol 7 (3) ◽

pp. 386-396 ◽

Cited By ~ 11

Author(s):

Y. Fujikoshi

Keyword(s):

Asymptotic Expansions ◽

Canonical Correlations ◽

Latent Roots

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Maximization of an Integral of a Matrix Function and Asymptotic Expansions of Distributions of Latent Roots of Two Matrices

The Annals of Statistics ◽

10.1214/aos/1176343554 ◽

1976 ◽

Vol 4 (4) ◽

pp. 796-806 ◽

Cited By ~ 5

Author(s):

A. K. Chattopadhyay ◽

K. C. S. Pillai ◽

Hung C. Li

Keyword(s):

Asymptotic Expansions ◽

Matrix Function ◽

Latent Roots

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On the Marginal Distributions of the Latent Roots of the Multivariate Beta Matrix

The Annals of Mathematical Statistics ◽

10.1214/aoms/1177692399 ◽

1972 ◽

Vol 43 (5) ◽

pp. 1664-1670 ◽

Cited By ~ 9

Author(s):

A. W. Davis

Keyword(s):

Marginal Distributions ◽

Beta Matrix ◽

Multivariate Beta ◽

Latent Roots

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